Some integral and asymptotic formulas associated with the Hurwitz zeta function (Q1883173)
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scientific article; zbMATH DE number 2105539
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some integral and asymptotic formulas associated with the Hurwitz zeta function |
scientific article; zbMATH DE number 2105539 |
Statements
Some integral and asymptotic formulas associated with the Hurwitz zeta function (English)
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1 October 2004
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The main object of this paper is to present an integral representation of the partial sum \(L_u(x, a)=\sum_{0\leq n\leq x}(n+a)^u\) of the Hurwitz zeta function \(\zeta(-u, a)\), which entails a number of implications for \(L_u(x, a)\) and \(\zeta(-u, a)\) and for their derivatives.
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Zeta-functions
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Explicit formulas
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Euler-Maclaurin summation formula
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Digamma function
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Incomplete gamma function
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Confluent hypergeometric function
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Generalized Stirling formula
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Generalized Euler constants
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Bernoulli polynomials
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